A Novel Ranking Function for Solving Single-Valued Trapezoidal Neutrosophic Transportation Problems Using the Zero-Point Method

Abstract

The transportation problem is one of the most widely studied special structures of linear programming, with extensive applications in supply-chain management, logistics and distribution planning. In realistic distribution environments the cost, availability and requirement parameters are rarely known with certainty; they are simultaneously affected by approval (truth), hesitation (indeterminacy) and rejection (falsity). The neutrosophic set, which models these three components independently, is therefore a more faithful tool than the classical fuzzy or intuitionistic fuzzy set. In this paper we study the transportation problem in which all parameters are single-valued trapezoidal neutrosophic numbers (SVTNNs). A novel ranking function is proposed that combines a generalised trapezoidal magnitude index with the neutrosophic score, thereby capturing both the spread of the trapezoid and the truth–indeterminacy–falsity confidence of each datum in a single real value. Using this ranking function the single-valued trapezoidal neutrosophic transportation problem (SVTNTP) is converted, in the first stage, into an equivalent crisp transportation problem; in the second stage the crisp problem is solved directly by the zero-point method. The optimality of the obtained solution is verified against the North-West Corner rule improved by the MODI (modified distribution) method. A numerical illustration with three sources and four destinations shows that the proposed procedure yields the optimal neutrosophic transportation cost in fewer and simpler steps than the classical two-phase approach, while requiring no additional optimality test.